Is there any way to subdivide the faces going around the edge of this so that the curve is smoother?
First of, you should recalculate normals that seem to be going inwards instead of outwards (notice the slight blueish tint instead of gray)


This is how correct normals look.


Next up is to make the mesh more smooth so press Ctrl+F and shade smooth in Edit mode (or can be done in the T panel in object mode aswell)


Without any other work whatsoever the mesh looks... uh.. ugly


However only by adding a correctly set up bevel modifier, you get very good results with not much more geometry.


This is the bevel modifier of the above, please note that Width is subject to object size and obviously this knife would be a bit too large^^


This is how the wireframe of the above looks.


Alternatively you can also get visibly beveled (not rounded) edges by using only 1 segment in Bevel and turning Auto Smooth on at about 30-60 degrees. (notice I have profile 0 here and that is not necessary, it can be the default 0.5 because at 1 segment setting the profile doesn't play a role)


This is the modifier setup of the above.


And this is wireframe of the above.